Boundary-only element solutions of 2D and 3D nonlinear and nonhomogeneous elastic problems

This paper presents a robust boundary element method (BEM) that can be used to solve elastic problems with nonlinearly varying material parameters, such as the functionally graded material (FGM) and damage mechanics problems. The main feature of this method is that no internal cells are required to evaluate domain integrals appearing in the conventional integral equations derived for these problems, and very few internal points are needed to improve the computational accuracy. In addition, one of the basic field quantities used in the boundary integral equations is normalized by the material parameter. As a result, no gradients of the field quantities are involved in the integral equations. Another advantage of using the normalized quantities is that no material parameters are included in the boundary integrals, so that a unified equation form can be established for multi-region problems which have different material parameters. This is very efficient for solving composite structural problems.